Question

By what acceleration, the wedge should move so that the block moves upwards along the surface of the wedge with an acceleration of $g\sin \theta$.

A. $2g\cos \theta$
B. $g\sin \theta$
C. $2g\tan \theta$
D. $g\cos \theta$

Answer 1

To construct a free-body diagram, we draw the point of concern, all forces acting on it, and resolve all force vectors into x– and y–components. A separate free-body diagram is required for each object in the question.

Complete step by step answer:
After drawing a free body diagram, we will get the following figure,

In the following question, we observe with respect to wedge. Hence, we apply pseudo force on the block. After substituting the values from free body diagram we will get,
$ma\cos \theta - mg\sin \theta = ma' \\\ \Rightarrow ma\cos \theta - mg\sin \theta = mg\sin \theta \\\ \Rightarrow a\cos \theta = 2g\sin \theta \\\ \Rightarrow a = \dfrac{{2g\sin \theta }}{{\cos \theta }} \\\ \therefore a = 2g\tan \theta \\\$
Hence, the correct option is C.

Note: Four forces are not often applied to objects. In certain cases, the number of forces described by a free-body diagram may be one, two, or three. In a free-body diagram, the number of forces that must be drawn is not a hard and fast rule. There is only one guideline to drawing free-body diagrams: reflect all of the forces that exist with that object in the given situation.